The injury-hit visitors came from behind at the Racecourse Ground to win 2-1 thanks to goals from James Constable and Ryan Williams in the space of two minutes.
It completed a superb run of away games, which have seen the U’s travel 1,200 miles in nine days to draw with Fleetwood in the league before Cup wins against Gateshead and Wrexham.
Wilder, who referred to pre-match comments from Wrexham striker Brett Ormerod saying the U’s had been fortunate to beat Gateshead, was again thrilled with the display.
He said: “We’ve clocked some miles up, but results and performances speak volumes to what we have got here.
“This was a tough old game. Apparently we have been very lucky in a couple of the games, but all you do is make sure you prepare and focus on the job in hand, which is to win football matches.
“I think we have deserved the result.”
He added: “We have done exceptionally well yet again.
“I thought we were outstanding in the second half, we passed the ball and really took the sting out of the game.
“Really, apart from when the referee decided to play two or three minutes extra at the end when they took unbelievable chances, we felt we were always pretty comfortable.”
Williams grabbed the winner with a close-range finish just after Constable’s low strike.
It was particularly satisfying for the winger, who had been booed all evening by the home fans.
They felt he had feigned injury in the first half, although television replays showed it was a nasty foul.
Williams said: “It’s always good when someone is giving you some stick to give it back to them.
“It was a really good feeling.
“Rosie (Danny Rose) told me to run to the near post, so I did, and it ended up bouncing straight to me, so I just nodded it into the net.
“I thought at the time (the tackle) was a straight red, but I can’t blame the ref, he mustn’t have had a good view.”
United netted £27,000 in prize money from the tie, taking their total earnings from the FA Cup run to £150,000.